UTe₂ is a promising candidate for spin-triplet superconductor, yet the nature of its superconducting state remains highly debated. Here, via scanning tunneling microscopy/spectroscopy, we observe a novel type of magnetic vortex with distinct dark-bright contrast in local density of states on UTe₂ (011) surface under a perpendicular magnetic field, resembling the conjugate structure of Yin-Yang diagram in Taoism. Each Yin-Yang vortex contains a quantized magnetic flux, and the boundary between the Yin and Yang parts aligns with the crystallographic a-axis of UTe₂. The vortex states exhibit intriguing behaviors –– a sharp zero-energy conductance peak exists at the Yang part, while a superconducting gap with pronounced coherence peaks exists at the Yin part, which is even sharper than those measured far from the vortex core or in the absence of magnetic field. Through theoretical analysis, we propose that the Yin-Yang vortex pattern on UTe₂ (011) surface arises from the vortex-induced asymmetric suppression of the surface states caused by the tilted Fermi surface. This physical picture is supported by our model calculations, which further constrain the possible d-vector orientations associated with the spin-triplet pairing. Therefore, the observation of Yin-Yang vortices constitutes robust and distinctive evidence for spin-triplet pairing in UTe₂, and provides new avenues for exploring the interplay between surface states and vortex bound states in topological superconductors.